What is keeping the translate arrows from working on the 3D Manipulator Tool
Snap to Grid is enabled (and the object is smaller than the grid)

The selection can be moved, you are just not providing an input that would be able to overcome the thereshold of the snap to increments.

If your object would have been 10 time bigger, you would now experiencing a stepping in using the grab tool, but as it's dimensions are small, you are not able to jump over the first step.

The solution would be to disable the "Snap suring transform" option.